Question

3.

x	y
-6	12
-5	14
-4	16
-3	18
-2	20

a. equation: ____________
b. how much will y be if the x values continue to 2? ____________
4.

x	y
-14	3
-12	6
-10	9
-8	12
-6	15

a. equation: ____________
b. how much will y be if the x value continues to -4? ____________
5.

hours	cost
5	20
5.5	30
6	40
6.5	50

a. equation: ____________
b. how much will the cost be at 9.5 hours? ____________
6.

hours	cost
5	25
5.5	30
6	35
6.5	40

a. equation: ____________
b. how much will the cost be at 7.5 hours? ____________

Explanation:

Problem 3

A. Equation

Step1: Find the slope ($m$)

Using two points \((-6, 12)\) and \((-5, 14)\), \(m=\frac{14 - 12}{-5-(-6)}=\frac{2}{1} = 2\)

Step2: Find the y - intercept ($b$)

Using point \((-6,12)\) and \(y=mx + b\), \(12=2\times(-6)+b\), \(12=-12 + b\), so \(b = 24\)

Step3: Write the equation

The equation is \(y = 2x+24\)

B. Find y when x = 2

Step1: Substitute x = 2 into the equation

Substitute \(x = 2\) into \(y=2x + 24\)

Step2: Calculate y

\(y=2\times2+24=4 + 24=28\)

Step1: Find the slope ($m$)

Using two points \((-14,3)\) and \((-12,6)\), \(m=\frac{6 - 3}{-12-(-14)}=\frac{3}{2}=1.5\)

Step2: Find the y - intercept ($b$)

Using point \((-14,3)\) and \(y=mx + b\), \(3 = 1.5\times(-14)+b\), \(3=-21 + b\), so \(b = 24\)

Step3: Write the equation

The equation is \(y = 1.5x+24\) or \(y=\frac{3}{2}x + 24\)

B. Find y when x=-4

Answer:

A. \(y = 2x+24\)
B. \(28\)

Problem 4

A. Equation